The question isn’t “should she learn to fight?”, it’s “how skilled do you expect her to be in a short period of time?”.
The answer to the question posed in the ask is both. She should focus on learning to fight and getting better at running away. Both are necessary survival skills. In fact, learning to run away is part of learning to fight. Learning to assess a situation to determine the threat level and decide when it is time to go. Learning to defuse situations to avoid a violent confrontation is also part of learning to fight.
Here’s the problem with the general outlook most people have on combat training. They think you’re learning to handle all the situations which come your way violently. That’s not it. You’re learning how to asses the situations to determine whether or not its within a range you can handle. The best warriors are the ones who know when to fight, when not to fight, when to call for backup, and when to leave.
Those skills are the ones she needs. It’s entirely possible to learn fighting as a defensive option when her other skills fall through. This is not someone who is going to be going at it with practiced swordsmen in a one on one duel, but might get good at cutting themselves free and learning how to create exits so they can find a safer position. They’re not particularly good at violence in the professional sense, but it works as a fallback when the situation grows desperate.
Combat is a skill set. With consistent practice she’ll get better at it and the more scenarios she’s thrown into then the faster she learns how to survive.
She’s going to spend a lot of time running away at first, which she will grow better at. Then, eventually, she’ll learn how to turn and fight. She’ll get better at that too as time passes. She’ll never be the equivalent of the team’s muscle, but that’s not the point. She may end up being a “fight only when I have to/last line of defense” character, but that works fine. I’m going to assume she has other skills she’s developed which are more useful to this merry band than her combat ability. Even if she doesn’t, she still works as a character. I mean, Merry and Pippen are some of the most beloved characters in The Lord of the Rings and they contribute almost nothing except moral support.
People play bards in Dungeons & Dragons. (Kidding, bard lovers, they’re awesome and can be incredibly deadly.)
The issues come when we start thinking a character needs to have certain qualities in order to be legitimate, rather than figuring out what their skill sets are and using those as the basis for how they solve problems.
Create a scenario and solve it based on what the character can do rather than what they can’t do. The assumption that a situation needs to be solved violently or that there’s only one outcome is faulty. Your story is in a character’s ability to problem solve, what the issue is and the way they went about finding a solution. Flattering your way out is just as legitimate as fighting, even more so as it draws less attention and creates fewer additional problems.
I’ve got a character who can do magic, but isn’t good enough to be a combat mage. She can’t really fight. When she and her friends were captured by giants, she was small enough to slip out through the cage bars. Since she wasn’t good at lockpicking and they were too far away to get help, she decided to go talk to the giants. The story evolved from there.
“If I can’t do X, what else can I do?”
That’s where the story is.
There are a variety of different skill ceilings with combat, levels of what you can do and can’t do. A person with a weekends self-defense training isn’t going to be tackling Navy Seals, but they’ll be better at identifying danger in their surroundings. They’ll be better at creating exits to so they can escape to safety. They may have a better chance when faced with danger.
You said it yourself, the point of this character training to fight isn’t so she can throw herself into the fray against seasoned combatants but to help her survive. Focus on that and keep track of her skill level versus that of her opponents.